Micro- and nanoelectromechanical systems (MEMS and NEMS, respectively) allow for the detection of chemical or biological compounds at extremely low detection thresholds, e.g. on the order of the attogram, when they are used as resonators. When an oscillating micro- or nanosystem interacts with a chemical or biological compound, the mechanical characteristics of the resonator may vary: measurement of a variation in the amplitude of the oscillator or of the variation in a frequency of a mode of the oscillator can make it possible to detect the compound or compounds.
Resonators of the MEMS and NEMS types have a higher aspect ratio than that of macroscopic resonators. An increase in the aspect ratio of a mechanical resonator favours the appearance of non-linear phenomena during the oscillation of the resonator (Postma, H. C., Kozinsky, I., Husain, A., & Roukes, M. L. (2005). Dynamic range of nanotube- and nanowire-based electromechanical systems. Applied Physics Letters, 86(22), 223105). Thus, for a wide range of amplitudes, a resonator at the micrometre or nanometre scale displays so-called “Duffing” behaviour, i.e. behaviour described by the following equation:
                                          x            ¨                    +                      Δ            ⁢                                                  ⁢            ω            ⁢                                                  ⁢                          x              .                                +                                    ω              0              2                        ⁢            x                    +                      γ            ⁢                                                  ⁢                          x              3                                      =                              F            L                    m                                    (        1        )            where x is the amplitude of the measured signal, ω0 is the pulse resonance, Δω is the dissipation related to the resonator's movement, FL is the force transduced to the resonator, m is the mass of the resonator, and γ is the non-linear coefficient, known as the “Duffing coefficient”. A person skilled in the art will find the known equation for a harmonic oscillator having a resonance that follows a Lorentzian curve, when the coefficient γ=0.
The non-linearity in an oscillator's behaviour leads to problems in implementing a detection function: an electromechanical transducer is typically a MEMS or NEMS oscillator able to operate in the linear regime. Otherwise, a mechanical bistability or hysteresis during an oscillation may compromise the transmission of a stimulus that is to be detected. Indeed, if the oscillation amplitude is not too large, a Duffing-type non-linearity (which obeys the Duffing equation) deforms the resonance and gives rise to a form of resonance known as Duffing-type resonance. If the oscillation amplitude is very large, the system enters a bistable regime which, in most applications, drastically compromises the transmission of a stimulus that is to be detected.
One solution to avoid non-linearities in the oscillations of the resonator may consist in exciting the resonator with forces that are weak enough to stay within the linear regime. In practice, the amplitude of the oscillations measured during resonance is often too weak to discriminate a signal from the measurement noise or to measure variations quantitatively.
Another solution consists in exciting a resonator with forces that can induce an amplitude large enough to be detected, but thereby also inducing non-linear behaviour, which must be corrected. A grid coupled to the resonator by electrical polarisation is used to compensate the non-linearities in the dynamics of the resonator (Kacem, N., Hentz, S., Pinto, D., Reig, B., & Nguyen, V. (2009). Non-linear dynamics of nanomechanical beam resonators: improving the performance of NEMS-based sensors. Nanotechnology, 20(27), 275501). When implementing this solution, numerical simulations that are costly in terms of calculations and time are necessary to find the appropriate experimental parameters for compensating non-linearities. In addition, the implementation of one or more grids must be tolerated by the resonator's mode of operation.
The present invention aims to overcome the aforementioned disadvantages of the prior art and, in particular, it aims to actuate the resonator in a given range of frequencies, close to its resonance frequency, proportionally to an excitation force, in the widest possible amplitude range and particularly in an amplitude range in which the resonator typically oscillates according to the so-called Duffing equation detailed above, while preserving its linearity, so that its mechanical resonance in this frequency range follows a Lorentzian curve and so that the detected signal is proportional to the injected signal.